Definition:Electric Flux

Definition

Let $\delta \mathbf S$ be an element of a vector area in an electric field whose strength is $\mathbf E$.

The electric flux through $\delta \mathbf S$ is defined as the dot product of $\mathbf E$ with $\delta \mathbf S$:

$\mathbf E \cdot \delta \mathbf S$

That is, by definition of dot product:

the magnitude $E$ of $\mathbf E$

multiplied by:

the projection of $\delta \mathbf S$ onto $\mathbf E$

That is:

$E \rdelta S \cos \psi$

where $\psi$ is the angle made by $\delta \mathbf S$ with $\mathbf E$.

Also see

• Results about electric flux can be found here.

Sources

• 1990: I.S. Grant and W.R. Phillips: Electromagnetism (2nd ed.) ... (previous) ... (next): Chapter $1$: Force and energy in electrostatics: $1.4$ Gauss's Law: $1.4.1$ The flux of a vector field